Algebra and Trigonometry with Analytic Geometry (With CD-ROM)

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Think of it as portable office hours! The Interactive Video Skillbuilder CD-ROM contains more than eight hours of video instruction. The problems worked during each video lesson are shown next to the viewing screen so that student can try working them before watching the solution. To help students evaluate their progress, each section contains a 10-question Web quiz (the results of which can be emailed to the instructor) and each chapter contains a chapter test, with answers to each problem on each test.

List of Graphing Calculator Topics

ix

Preface

xi

Fundamental Concepts of Algebra

1

(58)

Real Numbers

2

(17)

Exponents and Radicals

19

(12)

Algebraic Expressions

31

(14)

Fractional Expressions

45

(14)

Review Exercises

56

(2)

Discussion Exercises

58

(1)

Equations and Inequalities

59

(72)

Equations

60

(9)

Applied Problems

69

(11)

Quadratic Equations

80

(14)

Complex Numbers

94

(7)

Other Types of Equations

101

(9)

Inequalities

110

(9)

More on Inequalities

119

(12)

Review Exercises

127

(3)

Discussion Exercises

130

(1)

Functions and Graphs

131

(130)

Rectangular Coordinate Systems

132

(9)

Graphs of Equations

141

(16)

Lines

157

(18)

Definition of Function

175

(18)

Graphs of Functions

193

(16)

Quadratic Functions

209

(15)

Operations on Functions

224

(11)

Inverse Functions

235

(10)

Variation

245

(16)

Review Exercises

252

(6)

Discussion Exercises

258

(3)

Polynomial and Rational Functions

261

(64)

Polynomial Functions of Degree Greater Than 2

262

(11)

Properties of Division

273

(8)

Zeros of Polynomials

281

(14)

Complex and Rational Zeros of Polynomials

295

(8)

Rational Functions

303

(22)

Review Exercises

321

(2)

Discussion Exercises

323

(2)

Exponential and Logarithmic Functions

325

(66)

Exponential Functions

326

(12)

The Natural Exponential Function

338

(10)

Logarithmic Functions

348

(16)

Properties of Logarithms

364

(8)

Exponential and Logarithmic Equations

372

(19)

Review Exercises

385

(3)

Discussion Exercises

388

(3)

The Trigonometric Functions

391

(102)

Angles

392

(11)

Trigonometric Functions of Angels

403

(18)

Trigonometric Functions of Real Numbers

421

(19)

Values of the Trigonometric Functions

440

(8)

Trigonometric Graphs

448

(15)

Additional Trigonometric Graphs

463

(8)

Applied Problems

471

(22)

Review Exercises

484

(7)

Discussion Exercises

491

(2)

Analytic Trigonometry

493

(68)

Verifying Trigonometric Identities

494

(6)

Trigonometric Equations

500

(15)

The Addition and Substraction Formulas

515

(11)

Multiple-Angle Formulas

526

(10)

Product-to-Sum and Sum-to-Product Formulas

536

(5)

The Inverse Trigonometric Functions

541

(20)

Review Exercises

557

(3)

Discussion Exercises

560

(1)

Applications of Trigonometry

561

(64)

The Law of Sines

562

(10)

The Law of Cosines

572

(9)

Vectors

581

(15)

The Dot Product

596

(11)

Trigonometric Form for Complex Numbers

607

(7)

De Moivre's Theorem and nth Roots of Complex Numbers

614

(11)

Review Exercises

620

(4)

Discussion Exercises

624

(1)

Systems of Equations and Inequalities

625

(96)

Systems of Equations

626

(9)

Systems of Linear Equations in Two Variables

635

(9)

Systems of Inequalities

644

(9)

Linear Programming

653

(9)

Systems of Linear Equations in More Than Two Variables

662

(15)

The Algebra of Matrices

677

(10)

The Inverse of a Matrix

687

(7)

Determinants

694

(7)

Properties of Determinants

701

(8)

Partial Fractions

709

(12)

Review Exercises

715

(3)

Discussion Exercises

718

(3)

Sequences, Series, and Probability

721

(84)

Infinite Sequences and Summation Notation

722

(16)

Arithmetic Sequences

738

(7)

Geometric Sequences

745

(9)

Mathematical Induction

754

(7)

The Binomial Theorem

761

(9)

Permutations

770

(7)

Distinguishable Permutations and Combinations

777

(9)

Probability

786

(19)

Review Exercises

799

(3)

Discussion Exercises

802

(3)

Topics from Analytic Geometry

805

(78)

Parabolas

806

(10)

Ellipses

816

(14)

Hyperbolas

830

(12)

Plane Curves and Parametric Equations

842

(15)

Polar Coordinates

857

(16)

Polar Equations of Conics

873

(10)

Review Exercises

879

(2)

Discussion Exercises

881

(2)

Appendixes

883

I Common Graphs and Their Equations

884

II A Summary of Graph Transformations

886

III Graphs of Trigonometric Functions and Their Inverses

888

IV Values of the Trigonometric Functions of Special Angles on a Unit Circle